Parameter estimation and goodness-of-fit in log binomial regression
Parameter estimation and goodness-of-fit in log binomial regression
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DOI：
10.1002/bimj.200410165
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发表时间：
2006-02-01
影响因子：
1.7
通讯作者：
Hosmer, DW
中科院分区：
文献类型：
--
作者：
Blizzard, L;Hosmer, DW
调整混杂因素后的风险估计值可以从拟合的logistic回归模型中获得，但当结果并不罕见时，它会大大高估。对数二项式模型、二项式误差和对数链接正越来越多地用于这一目的。然而，该模型的性能，拟合优度测试和案例明智的诊断还没有研究。大量的模拟被用来比较对数二项式的性能，由Schouten等人（1993）提出的基于逻辑回归的方法和由Zou（2004）和Carter，Lipsitz和蒂利（2005）提出的泊松回归方法。对数二项回归导致“失败”率（不收敛，预测概率超出界限）高达59%。通过Schouten等人（1993年）的方法进行的估计得出，在对数二项式模型成功拟合的样本中，拟合对数二项式概率大于1的比例高达19%，在对数二项式模型拟合失败的样本中，拟合对数二项式概率大于1的比例高达78%。泊松回归方法观察到相似的百分比。三种模型的系数和标准误估计值相似。对数二项式拟合的拟合优度检验的拒绝率约为5%。当拟合不正确的逻辑回归模型时，拟合优度检验的效力是适度的。实例演示了方法的使用。不建议不加批判地使用对数二项回归模型。
An estimate of the risk, adjusted for confounders, can be obtained from a fitted logistic regression model, but it substantially over-estimates when the outcome is not rare. The log binomial model, binomial errors and log link, is increasingly being used for this purpose. However this model's performance, goodness of fit tests and case-wise diagnostics have not been studied. Extensive simulations are used to compare the performance of the log binomial, a logistic regression based method proposed by Schouten et al. (1993) and a Poisson regression approach proposed by Zou (2004) and Carter, Lipsitz, and Tilley (2005). Log binomial regression resulted in "failure" rates (non-convergence, out-of-bounds predicted probabilities) as high as 59%. Estimates by the method of Schouten et al. (1993) produced fitted log binomial probabilities greater than unity in up to 19% of samples to which a log binomial model had been successfully fit and in up to 78% of samples when the log binomial model fit failed. Similar percentages were observed for the Poisson regression approach. Coefficient and standard error estimates from the three models were similar. Rejection rates for goodness of fit tests for log binomial fit were around 5%. Power of goodness of fit tests was modest when an incorrect logistic regression model was fit. Examples demonstrate the use of the methods. Uncritical use of the log binomial regression model is not recommended.